Question 1 :
Choose the best possible option.<br>$\displaystyle{ x }^{ 3 }-5x+2{ x }^{ 2 }+1=0$ is quadraticequation.<br>
Question 2 :
Is the following equation quadratic?$n^{3}\, -\, n\, +\, 4\, =\, n^{3}$
Question 4 :
The number of solutions of the equation,$2\left\{ x \right\} ^{ 2 }+5\left\{ x \right\} -3=0$ is
Question 6 :
The roots of the following quadratic equations are real and distinct.<br/>$(x - 2a) (x - 2b) = 4ab$
Question 7 :
Find the values of $k$ for the following quadratic equation, so that they have two real and equal roots:$4x^2 - 2(k + 1)x + (k + 4) = 0$
Question 8 :
The given quadratic equations have real roots and roots are $\dfrac{\sqrt5}{3}, \, -\sqrt5$ :<br/> $3x^2 \, + \, 2\sqrt{5x} \, - \, 5 \, = \, 0$
Question 9 :
Does there exist a quadratic equation whose coefficients are all distinct irrationals but both the roots are rationals? Why?<br><br>
Question 10 :
If one of roots of $x^2+ ax + 4 = 0$ is twice the other root, then the value of 'a' is .
Question 11 :
$x^2-(m-3)x+m=0\:\:(m \in R)$ be a quadratic equation. Find the value of $m$ for which both the roots are greater than $2$
Question 12 :
Consider quadratic equation $ax^2+(2-a)x-2=0$, where $a \in R$.If exactly one root is negative, then the range of $a^2+2a+5$ is
Question 13 :
If $m_1$ and $m_2$ are the roots of the equation $x^2+\left(\sqrt{3}+2\right)x+\left(\sqrt{3}-1\right)=0$, then the area of the triangle formed by the lines $y=m_1x,y=m_2x$ and $y=2$ is :
Question 14 :
Find the values of $K$ so that the quadratic equations $x^2+2(K-1)x+K+5=0$ has atleast one positive root.
Question 15 :
If $\alpha$ and $\beta$ are roots of the equation $a{ x }^{ 2 }+bx+c=0$ then the equation whose roots are $\alpha +\frac { 1 }{ \beta }$ are $\beta +\frac { 1 }{ \alpha }$ is
